# Residual resultant over the projective plane and the implicitization problem

1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : In this article, we first generalize the recent notion of residual resultant of a complete intersection to the case of a local complete intersection of codimension 2 in the projective plane, which is the necessary and sufficient condition for a system of three polynomials to have a solution outside'' a variety, defined here by a local complete intersection of codimension 2. We give its degree in the coefficients of each polynomial and compute it as the gcd of three polynomials or as a product of two determinants divided by another one. In a second part we use this new type of resultant to give a new method to compute the implicit equation of a rational surface with base points in the case where these base points are a local complete intersection of codimension 2.
Document type :
Conference papers
Domain :

Cited literature [22 references]

https://hal.inria.fr/inria-00099846
Contributor : Laurent Busé <>
Submitted on : Tuesday, September 26, 2006 - 9:43:18 AM
Last modification on : Wednesday, December 11, 2019 - 10:34:11 PM
Long-term archiving on: Thursday, September 20, 2012 - 10:56:14 AM

### Identifiers

• HAL Id : inria-00099846, version 1

### Citation

Laurent Busé. Residual resultant over the projective plane and the implicitization problem. Internation Symposium on Symbolic and Algebraic Computing (ISSAC), Jul 2001, London, Ontario, Canada. pp.48--55. ⟨inria-00099846⟩

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